1950 AHSME Problems/Problem 18

Problem

Of the following

(1) $a(x-y)=ax-ay$

(2) $a^{x-y}=a^x-a^y$

(3) $\log (x-y)=\log x-\log y$

(4) $\frac{\log x}{\log y}=\log{x}-\log{y}$

(5) $a(xy)=ax\times ay$

$\textbf{(A)}\ \text{Only 1 and 4 are true}\qquad\\ \textbf{(B)}\ \text{Only 1 and 5 are true}\qquad\\ \textbf{(C)}\ \text{Only 1 and 3 are true}\qquad\\ \textbf{(D)}\ \text{Only 1 and 2 are true}\qquad\\ \textbf{(E)}\ \text{Only 1 is true}$

Solution

The distributive property doesn't apply to logarithms or in the ways illustrated, and only applies to addition and subtraction. Also, $a^{x-y} = \frac{a^x}{a^y}$ , so $\boxed{\textbf{(E)} \text{ Only 1 is true}}$ .

1950 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 17	Followed by Problem 19
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1950 AHSME Problems/Problem 18

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